An Empirical Characteristic Function Approach to VaR under a Mixture of Normal Distribution with Time-Varying Volatility
AbstractThis paper considers Value at Risk measures constructed under a discrete mixture of normal distribution on the innovations with time-varying volatility, or MN-GARCH, model. We adopt an approach based on the continuous empirical characteristic function to estimate the param eters of the model using several daily foreign exchange rates' return data. This approach has several advantages as a method for estimating the MN-GARCH model. In particular, under certain weighting measures, a closed form objective distance function for estimation is obtained. This reduces the computational burden considerably. In addition, the characteristic function, unlike its likelihood function counterpart, is always uniformly bounded over parameter space due to the Fourier transformation. To evaluate the VaR estimates obtained from alternative specifications, we construct several measures, such as the number of violations, the average size of violations, the sum square of violations and the expected size of violations. Based on these measures, we find that the VaR measures obtained from the MN-GARCH model outperform those obtained from other competing models.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University of Waterloo, Department of Economics in its series Working Papers with number 08008.
Date of creation: Dec 2008
Date of revision:
Value at Risk; Mixture of Normals; GARCH; Characteristic Function.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-01-03 (All new papers)
- NEP-ECM-2009-01-03 (Econometrics)
- NEP-RMG-2009-01-03 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
- Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(03), pages 691-721, June.
- Bauwens, L. & Bos, C.S. & van Dijk, H.K., 1999.
"Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk,"
Econometric Institute Research Papers
TI 99-082/4, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Luc Bauwens & Charles S. Bos & Herman K. van Dijk, 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Tinbergen Institute Discussion Papers 99-082/4, Tinbergen Institute.
- K. Van Dijk & Luc Bauwens & Charles Bos, 2000. "Adaptive Polar Sampling With An Application To A Bayes Measure Of Value-At-Risk," Computing in Economics and Finance 2000 145, Society for Computational Economics.
- BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K., 1999. "Adaptive polar sampling with an application to a Bayes measure of value-at-risk," CORE Discussion Papers 1999057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Markus Haas, 2004.
"Mixed Normal Conditional Heteroskedasticity,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 2(2), pages 211-250.
- Gray, Stephen F., 1996.
"Modeling the conditional distribution of interest rates as a regime-switching process,"
Journal of Financial Economics,
Elsevier, vol. 42(1), pages 27-62, September.
- Tom Doan, . "RATS programs to replicate Gray's 1996 Regime Switching GARCH paper," Statistical Software Components RTZ00080, Boston College Department of Economics.
- Jose A. Lopez, 1998.
"Methods for evaluating value-at-risk estimates,"
Economic Policy Review,
Federal Reserve Bank of New York, issue Oct, pages 119-124.
- Hamilton, James D. & Susmel, Raul, 1994.
"Autoregressive conditional heteroskedasticity and changes in regime,"
Journal of Econometrics,
Elsevier, vol. 64(1-2), pages 307-333.
- Tom Doan, . "RATS programs to estimate Hamilton-Susmel Markov Switching ARCH model," Statistical Software Components RTZ00083, Boston College Department of Economics.
- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
- Vlaar, Peter J G & Palm, Franz C, 1993. "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 351-60, July.
- Schwert, G William, 1989.
" Why Does Stock Market Volatility Change over Time?,"
Journal of Finance,
American Finance Association, vol. 44(5), pages 1115-53, December.
- G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- repec:fth:louvco:9957 is not listed on IDEAS
- Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009.
- Tony S. Wirjanto & Adam W. Kolkiewicz & Zhongxian Men, 2013. "Stochastic Conditional Duration Models with Mixture Processes," Working Paper Series 29_13, The Rimini Centre for Economic Analysis.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Pat Gruber).
If references are entirely missing, you can add them using this form.